Show that ANFA is NL-complete.

Short Answer

Expert verified

As (M=(Q,δ,q0,F,),w) It could take a little longer than log(|G,s,t|)can show output Q,δ,q0,F,and w throughout the process, log-space was used.

Step by step solution

01

Step-1: NL complete 

NL-complete is a complexity class in computational complexity theory that includes all languages that are complete for NL, a class of decision problems that can be handled by a nondeterministic Turing machine with a logarithmic amount of memory space. It is also easy to see teat there is a path from s to tiff there is an accepting run of A .

02

Step-2: ANFA is NL complete

To prove that ANFANL, It is built a nondeterministic turning machine that decides in log space:

Input: (M=(Q,δ,q0,F,),w)

Let

n=|w|,s=q0for    i=1,...,n

Assume newsδ(s,wi) where w is the ith character of w or.

If sFaccept, else reject.

To prove that ANFANLhard, ST-REACH is decreased, which is a well-known NL hard problem. As a result, a log-space transducer that accepts input G=(V,E),s,tis needed and output M,wsuch that (G,s,t)STREACH(M,w)ANFA.

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